In a medium saucepan, combine the milk, sugar, cornstarch, and salt. Heat over medium heat, stirring constantly, until the mixture thickens and comes to a boil.
Reduce the heat to low. In a separate bowl, beat the egg yolks. Slowly add about half of the hot milk mixture to the egg yolks, stirring constantly.
Pour the egg mixture back into the saucepan with the remaining milk mixture. Cook over low heat, stirring continuously, until the pudding thickens and reaches a creamy consistency.
Remove the saucepan from the heat. Add the butter and vanilla extract to the pudding, stirring until the butter is melted and fully incorporated.
Step 2: Assemble the Banana Pudding
In a serving dish or individual dessert cups, layer the pudding, sliced bananas, and cookies. Start with a layer of pudding, followed by a layer of banana slices, and then a layer of cookies. Repeat the layers until all the ingredients are used, ending with a layer of pudding on top.
Cover the pudding with plastic wrap, ensuring that the wrap touches the surface of the pudding to prevent a skin from forming. Refrigerate for at least 2 hours to allow the flavors to meld together and the pudding to set.
Step 3: Add the Whipped Cream and Serve
Just before serving, remove the pudding from the refrigerator. In a separate bowl, whip the cream until soft peaks form. If desired, add powdered sugar to sweeten the whipped cream.
Spread the whipped cream over the top of the chilled pudding, covering it completely.
Garnish with additional banana slices, if desired.
